Question

Determine the function f(x)= kx+m if f(x-1)-f(x)=2 and f(-2)=1-m

Answer 1

$f(x) = kx + m \\ f(x - 1) = k(x - 1) + m$

$f(x - 1) - f(x) = 2 \\ k(x - 1) + m - kx - m = 2 \\ kx - k + m - kx - m = 2 \\ - k = 2 \\ k = 2$

$f( - 2) = k( - 2) + m = 1 - m \\ k( - 2) + m = 1 - m \\ ( - 2)( - 2) + m = 1 - m \\ 4 + m = 1 - m \\ 2m = - 3 \\ m = \frac{ - 3}{2}$

$f(x) = - 2x - \frac{3}{2}$